Sellers with Misspecified Models

Principals often operate on the basis of misspecified models of their agents’ preferences. We show that even slight misspecification can often lead to large and non-vanishing losses. Instead we propose a two-step scheme, whereby: (i) the principal identifies the model-optimal menu; (ii) modifies prices by offering to share with the agent a fixed proportion of the profit she would receive if this item was sold at the model-optimal price. We show that her loss is bounded and vanishes smoothly as the model converges to the truth. Finally, two-step mechanisms without a sharing rule like (ii) will not yield a valid approximation.